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In a simply connected container containing a superfluid and rotating, there is a net circulation of superfluid. This is found due to the vortices formed, around which the superfluid rotates. These vortices have been found to generally form a triangular lattice arrangement. Why is the triangular lattice arrangement preferred by the vortices formed ?

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The long-range interaction between vortices is logarithmic (this is the same as the Coulomb interaction in 2d). The problem is simply to find the configuration that minimizes the total energy. This issue was first studied by Abrikosov, "On the magnetic properties of superconductors of the second group'', Sov. Phys. JETP 5, 1174 (1957). I never looked at the original paper -- apparently it actually gives the wrong answer, that the energy is minimized by a square lattice. The right answer, a triangular lattice, was found in W. H. Kleiner, L. M. Roth, and S. H. Autler, "Bulk solution of ginzburg-landau equations for type II superconductors: Upper critical fi eld region," Phys. Rev. 133, A1226 (1964).

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Out of curiosity, does the latter paper give any intuition or simple argument, or is it merely a matter of evaluating a complicated expression for all possible lattices and seeing which works best? – Chris White Jan 26 '14 at 2:49

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